Prime Numbers | 4 Aug 2009
 

List a set of prime numbers where the sum total of the complete set is 100.

Re: Prime Numbers | 4 Aug 2009
 

The sum of first 9 prime number is 100:

2
3
5
7
11
13
17
19
23

Re: Prime Numbers | 4 Aug 2009
 

Well there are other possiblities too..but im just considering the first set n obviously the easier one to figure out... :P

Re: Prime Numbers | 4 Aug 2009
 

97 and 3

Re: Prime Numbers | 4 Aug 2009
 

The first (and smallest) set that I could think of immediately was 97+3.
But, your answer is acceptable too.
So, congrats :)

Re: Prime Numbers | 4 Aug 2009
 

Thanks saswat :)

Re: Prime Numbers | 4 Aug 2009
 

Listings all possible sets that I could think of :)

03 97
11 89
02 03 05 07 83
02 03 05 11 79
02 03 05 17 73
02 03 05 19 71
02 07 11 13 67
02 07 13 17 61
02 07 11 19 61
02 03 05 07 11 13 59
02 03 05 07 13 17 53
02 03 05 11 13 19 47
03 05 13 17 19 43
02 03 05 13 17 19 41
03 11 13 17 19 37
02 07 11 13 17 19 31
02 03 05 07 11 13 17 19 23
05 07 17 19 23 29
07 11 13 17 23 29

Re: Prime Numbers | 4 Aug 2009
 

This are the first 9 prime numbers as well which when verifying yesterdays sum hit as 100. So formed this one.

Re: Prime Numbers | 4 Aug 2009
 

Congrats rik

Re: Prime Numbers | 4 Aug 2009
 

OK, now that I have coded my own super-fast generator, I would like to mention that this list is far from complete, the complete list has 233 different sets. The list is :

--> { 3, 97 }
--> { 11, 89 }
--> { 17, 83 }
--> { 29, 71 }
--> { 41, 59 }
--> { 47, 53 }
--> { 2, 19, 79 }
--> { 2, 31, 67 }
--> { 2, 37, 61 }
--> { 3, 5, 13, 79 }
--> { 3, 5, 19, 73 }
--> { 3, 5, 31, 61 }
--> { 3, 7, 11, 79 }
--> { 3, 7, 17, 73 }
--> { 3, 7, 19, 71 }
--> { 3, 7, 23, 67 }
--> { 3, 7, 29, 61 }
--> { 3, 7, 31, 59 }
--> { 3, 7, 37, 53 }
--> { 3, 7, 43, 47 }
--> { 3, 11, 13, 73 }
--> { 3, 11, 19, 67 }
--> { 3, 11, 43, 43 }
--> { 3, 13, 17, 67 }
--> { 3, 13, 23, 61 }
--> { 3, 13, 31, 53 }
--> { 3, 13, 37, 47 }
--> { 3, 13, 41, 43 }
--> { 3, 17, 19, 61 }
--> { 3, 17, 37, 43 }
--> { 3, 19, 31, 47 }
--> { 3, 19, 37, 41 }
--> { 3, 23, 31, 43 }
--> { 3, 23, 37, 37 }
--> { 3, 29, 31, 37 }
--> { 5, 7, 17, 71 }
--> { 5, 7, 29, 59 }
--> { 5, 7, 41, 47 }
--> { 5, 11, 13, 71 }
--> { 5, 11, 17, 67 }
--> { 5, 11, 23, 61 }
--> { 5, 11, 31, 53 }
--> { 5, 11, 37, 47 }
--> { 5, 11, 41, 43 }
--> { 5, 13, 23, 59 }
--> { 5, 13, 29, 53 }
--> { 5, 13, 41, 41 }
--> { 5, 17, 19, 59 }
--> { 5, 17, 31, 47 }
--> { 5, 17, 37, 41 }
--> { 5, 19, 23, 53 }
--> { 5, 19, 29, 47 }
--> { 5, 23, 29, 43 }
--> { 5, 23, 31, 41 }
--> { 7, 11, 23, 59 }
--> { 7, 11, 29, 53 }
--> { 7, 11, 41, 41 }
--> { 7, 13, 19, 61 }
--> { 7, 13, 37, 43 }
--> { 7, 17, 23, 53 }
--> { 7, 17, 29, 47 }
--> { 7, 19, 31, 43 }
--> { 7, 19, 37, 37 }
--> { 7, 23, 29, 41 }
--> { 11, 13, 17, 59 }
--> { 11, 13, 23, 53 }
--> { 11, 13, 29, 47 }
--> { 11, 17, 19, 53 }
--> { 11, 17, 29, 43 }
--> { 11, 17, 31, 41 }
--> { 11, 19, 23, 47 }
--> { 11, 19, 29, 41 }
--> { 11, 23, 29, 37 }
--> { 13, 17, 23, 47 }
--> { 13, 17, 29, 41 }
--> { 13, 19, 31, 37 }
--> { 17, 19, 23, 41 }
--> { 17, 23, 29, 31 }
--> { 19, 23, 29, 29 }
--> { 2, 3, 5, 7, 83 }
--> { 2, 3, 5, 11, 79 }
--> { 2, 3, 5, 17, 73 }
--> { 2, 3, 5, 19, 71 }
--> { 2, 3, 5, 23, 67 }
--> { 2, 3, 5, 29, 61 }
--> { 2, 3, 5, 31, 59 }
--> { 2, 3, 5, 37, 53 }
--> { 2, 3, 5, 43, 47 }
--> { 2, 3, 7, 17, 71 }
--> { 2, 3, 7, 29, 59 }
--> { 2, 3, 7, 41, 47 }
--> { 2, 3, 11, 13, 71 }
--> { 2, 3, 11, 17, 67 }
--> { 2, 3, 11, 23, 61 }
--> { 2, 3, 11, 31, 53 }
--> { 2, 3, 11, 37, 47 }
--> { 2, 3, 11, 41, 43 }
--> { 2, 3, 13, 23, 59 }
--> { 2, 3, 13, 29, 53 }
--> { 2, 3, 13, 41, 41 }
--> { 2, 3, 17, 19, 59 }
--> { 2, 3, 17, 31, 47 }
--> { 2, 3, 17, 37, 41 }
--> { 2, 3, 19, 23, 53 }
--> { 2, 3, 19, 29, 47 }
--> { 2, 3, 23, 29, 43 }
--> { 2, 3, 23, 31, 41 }
--> { 2, 5, 7, 13, 73 }
--> { 2, 5, 7, 19, 67 }
--> { 2, 5, 7, 43, 43 }
--> { 2, 5, 11, 23, 59 }
--> { 2, 5, 11, 29, 53 }
--> { 2, 5, 11, 41, 41 }
--> { 2, 5, 13, 19, 61 }
--> { 2, 5, 13, 37, 43 }
--> { 2, 5, 17, 23, 53 }
--> { 2, 5, 17, 29, 47 }
--> { 2, 5, 19, 31, 43 }
--> { 2, 5, 19, 37, 37 }
--> { 2, 5, 23, 29, 41 }
--> { 2, 7, 11, 13, 67 }
--> { 2, 7, 11, 19, 61 }
--> { 2, 7, 11, 37, 43 }
--> { 2, 7, 13, 17, 61 }
--> { 2, 7, 13, 19, 59 }
--> { 2, 7, 13, 31, 47 }
--> { 2, 7, 13, 37, 41 }
--> { 2, 7, 17, 31, 43 }
--> { 2, 7, 17, 37, 37 }
--> { 2, 7, 19, 29, 43 }
--> { 2, 7, 19, 31, 41 }
--> { 2, 7, 23, 31, 37 }
--> { 2, 7, 29, 31, 31 }
--> { 2, 11, 13, 31, 43 }
--> { 2, 11, 13, 37, 37 }
--> { 2, 11, 17, 23, 47 }
--> { 2, 11, 17, 29, 41 }
--> { 2, 11, 19, 31, 37 }
--> { 2, 13, 17, 31, 37 }
--> { 2, 13, 19, 23, 43 }
--> { 2, 13, 19, 29, 37 }
--> { 2, 13, 23, 31, 31 }
--> { 2, 17, 19, 31, 31 }
--> { 2, 17, 23, 29, 29 }
--> { 3, 5, 7, 11, 13, 61 }
--> { 3, 5, 7, 11, 31, 43 }
--> { 3, 5, 7, 11, 37, 37 }
--> { 3, 5, 7, 13, 19, 53 }
--> { 3, 5, 7, 13, 29, 43 }
--> { 3, 5, 7, 13, 31, 41 }
--> { 3, 5, 7, 17, 31, 37 }
--> { 3, 5, 7, 19, 23, 43 }
--> { 3, 5, 7, 19, 29, 37 }
--> { 3, 5, 7, 23, 31, 31 }
--> { 3, 5, 11, 13, 31, 37 }
--> { 3, 5, 11, 17, 23, 41 }
--> { 3, 5, 11, 19, 31, 31 }
--> { 3, 5, 11, 23, 29, 29 }
--> { 3, 5, 13, 17, 19, 43 }
--> { 3, 5, 13, 17, 31, 31 }
--> { 3, 5, 13, 19, 23, 37 }
--> { 3, 5, 13, 19, 29, 31 }
--> { 3, 7, 11, 13, 19, 47 }
--> { 3, 7, 11, 13, 23, 43 }
--> { 3, 7, 11, 13, 29, 37 }
--> { 3, 7, 11, 17, 19, 43 }
--> { 3, 7, 11, 17, 31, 31 }
--> { 3, 7, 11, 19, 23, 37 }
--> { 3, 7, 11, 19, 29, 31 }
--> { 3, 7, 13, 17, 19, 41 }
--> { 3, 7, 13, 17, 23, 37 }
--> { 3, 7, 13, 17, 29, 31 }
--> { 3, 7, 13, 19, 29, 29 }
--> { 3, 7, 17, 19, 23, 31 }
--> { 3, 11, 13, 17, 19, 37 }
--> { 3, 11, 13, 19, 23, 31 }
--> { 5, 7, 11, 13, 17, 47 }
--> { 5, 7, 11, 13, 23, 41 }
--> { 5, 7, 11, 17, 19, 41 }
--> { 5, 7, 11, 17, 23, 37 }
--> { 5, 7, 11, 17, 29, 31 }
--> { 5, 7, 11, 19, 29, 29 }
--> { 5, 7, 13, 17, 29, 29 }
--> { 5, 7, 17, 19, 23, 29 }
--> { 5, 11, 13, 17, 23, 31 }
--> { 5, 11, 13, 19, 23, 29 }
--> { 5, 13, 17, 19, 23, 23 }
--> { 7, 11, 13, 17, 23, 29 }
--> { 7, 11, 17, 19, 23, 23 }
--> { 2, 3, 5, 7, 11, 13, 59 }
--> { 2, 3, 5, 7, 11, 19, 53 }
--> { 2, 3, 5, 7, 11, 29, 43 }
--> { 2, 3, 5, 7, 11, 31, 41 }
--> { 2, 3, 5, 7, 13, 17, 53 }
--> { 2, 3, 5, 7, 13, 23, 47 }
--> { 2, 3, 5, 7, 13, 29, 41 }
--> { 2, 3, 5, 7, 17, 19, 47 }
--> { 2, 3, 5, 7, 17, 23, 43 }
--> { 2, 3, 5, 7, 17, 29, 37 }
--> { 2, 3, 5, 7, 19, 23, 41 }
--> { 2, 3, 5, 7, 23, 29, 31 }
--> { 2, 3, 5, 11, 13, 19, 47 }
--> { 2, 3, 5, 11, 13, 23, 43 }
--> { 2, 3, 5, 11, 13, 29, 37 }
--> { 2, 3, 5, 11, 17, 19, 43 }
--> { 2, 3, 5, 11, 17, 31, 31 }
--> { 2, 3, 5, 11, 19, 23, 37 }
--> { 2, 3, 5, 11, 19, 29, 31 }
--> { 2, 3, 5, 13, 17, 19, 41 }
--> { 2, 3, 5, 13, 17, 23, 37 }
--> { 2, 3, 5, 13, 17, 29, 31 }
--> { 2, 3, 5, 13, 19, 29, 29 }
--> { 2, 3, 5, 17, 19, 23, 31 }
--> { 2, 3, 7, 11, 13, 17, 47 }
--> { 2, 3, 7, 11, 13, 23, 41 }
--> { 2, 3, 7, 11, 17, 19, 41 }
--> { 2, 3, 7, 11, 17, 23, 37 }
--> { 2, 3, 7, 11, 17, 29, 31 }
--> { 2, 3, 7, 11, 19, 29, 29 }
--> { 2, 3, 7, 13, 17, 29, 29 }
--> { 2, 3, 7, 17, 19, 23, 29 }
--> { 2, 3, 11, 13, 17, 23, 31 }
--> { 2, 3, 11, 13, 19, 23, 29 }
--> { 2, 3, 13, 17, 19, 23, 23 }
--> { 2, 5, 7, 11, 13, 19, 43 }
--> { 2, 5, 7, 11, 13, 31, 31 }
--> { 2, 5, 7, 11, 17, 29, 29 }
--> { 2, 5, 7, 13, 17, 19, 37 }
--> { 2, 5, 7, 13, 19, 23, 31 }
--> { 2, 5, 11, 13, 17, 23, 29 }
--> { 2, 5, 11, 17, 19, 23, 23 }
--> { 2, 7, 11, 13, 17, 19, 31 }
--> { 2, 3, 5, 7, 11, 13, 17, 19, 23 }

If anyone wants the source, I can share it here :D